Pairs without leftovers
Even numbers pair up completely. Odd numbers never do.
Dancing in pairs
Nine children want to dance. Every dance needs two children: a pair. Each child must have exactly one partner.
What happens with 9 children?
What this lesson covers
The idea
An even number can be arranged in pairs without any leftovers; an odd number cannot, being one more than a collection of pairs. The property of being even or odd is called parity.
Dancing in pairs
Nine children want to dance. Every dance needs two children: a pair. Each child must have exactly one partner.
What happens with 9 children?
- Everyone finds a partner
- One child is left without a partner
- Two children are left without partners
Pair up the dots
Each dot is a child. Tap a dot to give it a partner, and keep going. Then say whether the number is even or odd.
Pairs, with or without a leftover
Some numbers pair up completely. Some always have one dot left over, however you pair.
An odd number is one more than a collection of pairs. The property of being even or odd is called parity.
An even number can be arranged in pairs without any leftovers. An odd number cannot: it is one more than a collection of pairs. Being even or odd is called parity.
- Number | In pairs
- 12 | 6 pairs, none left
- 14 | 7 pairs, none left
- 7 | 3 pairs and 1 left
- 9 | 4 pairs and 1 left
Notes
An even number can be arranged in pairs without any leftovers. An odd number cannot: it is one more than a collection of pairs. Being even or odd is called parity.
Check yourself
A number is arranged in pairs. There are 6 pairs and 1 dot left over. What is the number?
Answer: 13
6 pairs = 6 × 2 = 12 dots, plus 1 left over: 13. It is odd.
Which of these can be arranged in pairs without any leftover?
A newspaper says: “14,70,369 people got married last year.” A friend says: “Wait, shouldn’t it be an even number?” Why does the friend say so?
15 laddus are put on plates two at a time. After all the pairs are made, how many laddus are left over?
Answer: 1
7 pairs use 14 laddus. 15 − 14 = 1 laddu is left over, so 15 is odd.
- 25. 25 = 12 pairs and 1 left over, so it is odd.
- 31. 31 = 15 pairs and 1 left over, so it is odd.
- 38 — correct. Yes! 38 = 19 pairs, nothing left over, so it is even.
- 47. 47 = 23 pairs and 1 left over, so it is odd.
- People marry in pairs, so all of them should be arrangeable in pairs with no one left over — correct. Yes! 14,70,369 has one left over, so it is odd. That cannot be a count of people who married each other.
- Every big number is even. No. Big numbers can be odd too. 14,70,369 is odd.
- Newspapers always print even numbers. Nothing says that. The friend is thinking about pairs.